$$\text { Set up the iterated integral for evaluating } \iint _ { D } \int f ( r , \theta , z ) d z r d r d \theta \text { over the given region D. }$$

question 217

Multiple Choice

$$\text { Set up the iterated integral for evaluating } \iint _ { D } \int f ( r , \theta , z ) d z r d r d \theta \text { over the given region D. }$$
- $\mathrm { D }$ is the solid right cylinder whose base is the region between the circles $r = 7 \cos \theta$ and $r = 8 \cos \theta$ , and whose top lies in the plane $z = 9 - y$ .

• A) \(\int _ { 0 } ^ { 2 \pi } \int _ { 7 \cos \theta } ^ { 8 \cos \theta } \int _ { 0 } ^ { 9 - r \sin \theta } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta\)
• B) \(\int _ { 0 } ^ { \pi } \int _ { 7 \cos \theta } ^ { 8 \cos \theta } \int _ { 0 } ^ { 9 - \sin \theta } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } r \mathrm { dr } d \theta\)
• C) \(\int _ { 0 } ^ { 2 \pi } \int _ { 7 } ^ { 8 \cos \theta } \int _ { 0 } ^ { 9 - \sin \theta } \mathrm { cos } \theta ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta\)
• D) \(\int _ { 0 } ^ { \pi } \int _ { 7 } ^ { 8 \cos \theta } \int _ { 0 } ^ { 9 - r \sin \theta } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta\)

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